Encouraging Students to Persist Through Challenges

Use place value understanding and properties of operations to add and subtract

7

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Encouraging Students to Persist Through Challenges Transcript
Speaker 1: Today we will work harder to get smarter. Growth mindset means believing that your brain has the capacity to grow. My job as a teacher is to teach my students strategies to help them grow their brains.
Oh my goodness. Way to be so precise and clear.
Are we taking away two, one, or eight?
Speaker 2: Eight.
Speaker 1: In life, students are going to need to pursue problems and they're going to need to be developed as problem solvers who know how to encounter a challenge and work through it to persevere to solve it.
Speaker 3: How many star stickers did Sally have left?
Speaker 1: Scholars, remind our brains how we solve this. Turn and tell your partner, "I solved this problem by..."
In math, in particular, I'm much more concerned with their ability to make sense of a problem and persevere in solving it than I am in them getting the right answer.
How many more do I need to take away?
Speaker 4: Eight.
Speaker 5: Eight.
Speaker 1: Eight. How do you know?
Speaker 4: Because it said right there, 248.
Speaker 1: Today's lesson was a number's sense lesson and students were tasked with subtracting three digit numbers in story problems.
Mathematicians, that problem felt especially challenging, didn't it?
Speaker 6: Yes.
Speaker 1: One thing you saw in my class today was my students encounter a challenging problem and really embrace it and get excited.
What felt challenging about that? Brenda?
Brenda: I got stuck on the 30 part -
Speaker 1: I almost normalize that everyone's going to feel stuck, everyone's going to feel challenged by it so that they can get excited and think about the strategies they can implement to tackle the problem.
What can you do when you're feeling stuck?
Brenda: Can I have some help, I'm feeling stuck about taking away two more tens?
Speaker 1: Way to be specific, Brenda, about how to get help. Justify.
Speaker 7: I took a jump of two and that got me to 200.
Speaker 1: Justifying and critiquing is one of the most critical components I can give my students to enable their ability to pursue a challenge.
Speaker 8: I solved that problem by doing the sticker notation and then...
Speaker 1: That means they're explaining their thinking with reasoning and evidence and they're asking others to explain their thinking as well to better understand.
Speaker 9: I figured it out by doing one strip and...
Speaker 10: What do you mean one strip?
Speaker 1: When we are tasked with the ability to express ourselves or articulate our thinking, it really illuminates our understanding or our misunderstanding.
Speaker 11: 30, 40, and 48.
Speaker 12: Can you explain more about [?]?
Speaker 11: Yeah, I did it a different way.
Speaker 1: So when we're asking students to justify their thinking, explain their thinking, sometimes you can see that there are some gaps or some holes.
Speaker 13: Hey, that makes two.
Speaker 14: 502.
Speaker 16: 502. I think you're trying to say 522.
Speaker 1: When you invite that into a classroom setting you're allowing for feedback from other scholars to engage in that thinking, whether they're understanding or misunderstanding it.
Speaker 17: [?].
Speaker 18: I disagree with you because we should do a strategy like adding up -
Speaker 1: I think it really raises the level of rigor in a classroom when students can understand their processing and can also question and understand others.
Christian and [?] were having kind of a heated discussion about the most efficient strategy to use to solve this problem. Go ahead Christian.
Christian: I took a jump of 60.
Speaker 1: My strategy was?
Christian: Adding up the two questions so that I -
Speaker 19: Why do you take a jump that would make a funny number?
Christian: I know that 60 plus 1 equals 61.
Speaker 1: I just want to pause and reflect on what's going on here. Already two people have shared out the same strategy but they did it in a different way. Is there another way you can use the tool?
One of the ways I feel like I've made a challenge feel exciting is even just through the strategy wait time.
Are these worth the same as this?
When I see a student struggling I really zero in on that and I capitalize on it. I say, "Oh my goodness. I can really see the wheels in your brain spinning."
What tool would help me solve this problem. Is a linking cube the right tool?
Speaker 20: No.
Speaker 1: So think. What may be a better tool to use?
Speaker 20: When it's tens and ones -
Speaker 1: Hundreds, tens and ones. Justify.
Speaker 20: Because I have three digit numbers.
Speaker 1: Great.
Speaker 21: There's two ones so I think that's 522.
Speaker 1: We haven't even found the answer yet, have we? How are you feeling?
Speaker 20: Good.
Speaker 21: Great.
Speaker 1: Even though you haven't found the answer?
Speaker 20: Yeah.
Speaker 1: Why?
Speaker 20: Because I'm working so hard.
Speaker 1: Okay, friends I'm going to have to stop you. We ran out of time here. We're doing so much thinking.
Mathematicians, I saw groups talking about different problems. At the green table, we haven't even solved the first problem but do you know what, they looked so happy. Can you tell the class about it.
Speaker 22: We didn't know how to figure it out but when it was time to go to lunch we didn't quit, we were happy because we were growing our brain.
Speaker 1: Those of you at your desks, give a nod if that feels like what you are feeling right now.
This process is probably one of the most exciting things I find about being a teacher.
She's saying me too.
Seeing my students struggle and encounter a challenge and embrace it is something that leaves me with great peace of mind because I know that when they leave my classroom they'll continue to have that growth mindset, they'll carry it on with them as they undoubtedly experience new challenges in life.
Speaker 23: Taking charge of my own learning.

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